Need some help

[MHoydilla]

Ok here is the problem if we have 7 independant events all with 2 outcomes, yes or no. If the probability of any one event is 94% = no and 6% = yes. If I run these 7 events what are the chances of having 0,1,2,3,4,5,6, or 7 end with a yes result(7 would mean 7 yes and 0 no's total). Now if I change the probability of yes to 7%, or 8% what are the chances or 1,2,3,4,5,6, or 7 that with a yes result.

[AaronBrown]

The table below might be hard to read, but you can cut and paste it into Excel and use "Text to Columns" to fix it. The three columns show the probabilities of the number of "yeses" on the left, for 6%, 7% and 8% probability of "yes" respectively.

This is a simple application of the binomial distribution.

6% 7% 8%
0 0.6484775942 0.6017008706 0.5578466012
1 0.2897453080 0.3170251899 0.3395588008
2 0.0554831441 0.0715863332 0.0885805567
3 0.0059024621 0.0089803644 0.0128377618
4 0.0003767529 0.0006759414 0.0011163271
5 0.0000144288 0.0000305264 0.0000582432
6 0.0000003070 0.0000007659 0.0000016882
7 0.0000000028 0.0000000082 0.0000000210
Total 1.00 1.00 1.00
Mean 0.42 0.49 0.56

[MHoydilla]

That chart was perfect, is there any chance you could post the same chart with 10 events, with 6,7, and 8%.

[BruceZ]

[ QUOTE ]
That chart was perfect, is there any chance you could post the same chart with 10 events, with 6,7, and 8%.

[/ QUOTE ]

It's past Aaron's bedtime, so night shift's responding: /images/graemlins/wink.gif

Here are both tables. The first one matches Aaron's.

If it appears to anyone that these tables are not formatted properly, let me know. To me they look right, but that may depend on browser settings, fonts, tabs, etc. The percents, totals, and mean should appear approximately in the center of each column.

<font class="small">Code:</font><hr /><pre>
6% 7% 8%
0 0.6484775942 0.6017008706 0.5578466012
1 0.2897453080 0.3170251899 0.3395588008
2 0.0554831441 0.0715863332 0.0885805567
3 0.0059024621 0.0089803644 0.0128377618
4 0.0003767529 0.0006759414 0.0011163271
5 0.0000144288 0.0000305264 0.0000582432
6 0.0000003070 0.0000007659 0.0000016882
7 0.0000000028 0.0000000082 0.0000000210
total 1.00 1.00 1.00
mean 0.42 0.49 0.56

6% 7% 8%
0 0.5386151141 0.4839823072 0.4343884542
1 0.3437968813 0.3642877581 0.3777290906
2 0.0987501680 0.1233877890 0.1478070355
3 0.0168085392 0.0247660078 0.0342740952
4 0.0018775496 0.0032621892 0.0052156232
5 0.0001438123 0.0002946493 0.0005442389
6 0.0000076496 0.0000184816 0.0000394376
7 0.0000002790 0.0000007949 0.0000019596
8 0.0000000067 0.0000000224 0.0000000639
9 0.0000000001 0.0000000004 0.0000000012
10 0.0000000000 0.0000000000 0.0000000000
total 1.00 1.00 1.00
mean 0.60 0.70 0.80
</pre><hr />

The formula for each cell in the second table is Combin(10,n)*p^n*(1-p)^(10-n) where n is the number of yeses from the first column, and p is 6%, 7%, or 8%. For the first table, change the 10s to 7s.